Problem: Simplify the following expression: $ r = \dfrac{-7}{4} + \dfrac{y - 3}{3y} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3y}{3y}$ $ \dfrac{-7}{4} \times \dfrac{3y}{3y} = \dfrac{-21y}{12y} $ Multiply the second expression by $\dfrac{4}{4}$ $ \dfrac{y - 3}{3y} \times \dfrac{4}{4} = \dfrac{4y - 12}{12y} $ Therefore $ r = \dfrac{-21y}{12y} + \dfrac{4y - 12}{12y} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{-21y + 4y - 12}{12y} $ $r = \dfrac{-17y - 12}{12y}$